Movie Rating Model and Predictor

Part 1: Data

The data were comprised of audience and critics opinions, awards, studio, and actor information from Rotten Tomatoes, imdb, and BoxOfficeMojo.com for a random sample of 651 movies produced and released prior to 2016.

Data Sources

Rotten Tomatoes

Launched in August 1998 by Senh Duong, Rotten Tomatoes is an American review aggregation website for film and television.

IMDB

Generalizability

Data Preprocessing

As a first step, variables such as website addresses and film titles were removed from the data set, then some 619 completed cases were extracted for downstream analysis. Since the focus was on theatrical releases, TV movies were excised from the data set. Next, three additional data sets were created:
* Film Box Office * Director Profiles
* Actor Profiles

Film Box Office The overarching aim was to understand which factors most influenced box office success for a film. Since box office revenue was not among the features provided in the data set, the first preprocessing step was to identify (or create) a response variable that would correlate with box office success. As such, total box office was obtained from the BoxOfficeMojo.com site for a random sampling of some 230 films from the original sample. The first step in the bivariate analysis was to identify which of the provided variables (or variables derived from those provided) most correlated with box office success.

Director / Actor Profiles: The purpose of the director/actor profiles was to capture the experience and popularity of each director and actor. The experience variables were simply the total number of films in the sample in which the director or actor was listed in the original sample. Popularity, in the director’s case was the sum of the IMDB votes for the director’s films. Similarly, the popularity for an actor was the sum of the allocated IMDB votes for films in which the actor was listed as one of the top 5. Actors were allocated IMDB votes as follows:
* 40% of total film IMDB votes for actor1
* 30% of total film IMDB votes for actor2
* 15% of total film IMDB votes for actor3
* 10% of total film IMDB votes for actor4
* 5% of total film IMDB votes for actor5
These variables were then merged into the main sample data set.

Variables Added A variable was created to capture the number of days between theatrical and dvd release. A composite score variable defined as 10 * IMDB Rating + critics score + audience_score was created and lastly, log transformations were applied to certain variables such as IMDB and cast votes. To sum, the following variables listed in Table 1 were added to the data set.
Table 1: Variables added to the data set
Variable Description
box_office Box office revenue from BoxOfficeMojo.com
box_office_log Log of Box office revenue from BoxOfficeMojo.com
cast_experience The sum across all cast members for a film, of the number of films in which each actor appeared
cast_experience_log Log of the sum across all cast members for a film, of the number of films in which each actor appeared
cast_votes Total number of allocated IMDB votes for the cast of a film
cast_votes_log Log of the total number of allocated IMDB votes for the cast of a film
director_experience Total number of films in sample for a director
director_experience_log Log total number of films in sample for a director
imdb_num_votes_log Log number of IMDB votes
runtime_log Log runtime of movie (in minutes)
scores 10 * IMDB Rating + critics score + audience_score
scores_log Log(10 * IMDB Rating + critics score + audience_score)
thtr_days Number of days between theatre and dvd release
thtr_days_log Log number of days between theatre and dvd release
thtr_rel_season Season the movie was released in theaters
Variables Removed The following variables listed in Table 2 were removed from the data set for the reasons listed below.
Table 2: Variables removed from the data set
Variable Description Rationale
actor1 First main actor/actress in the abridged cast of the movie Not predictive without other data
actor2 Second main actor/actress in the abridged cast of the movie Not predictive without other data
actor3 Third main actor/actress in the abridged cast of the movie Not predictive without other data
actor4 Fourth main actor/actress in the abridged cast of the movie Not predictive without other data
actor5 Fifth main actor/actress in the abridged cast of the movie Not predictive without other data
audience_rating Categorical variable for audience rating on Rotten Tomatoes (Spilled, Upright) Redundant with audience_score
critics_rating Categorical variable for critics rating on Rotten Tomatoes (Certified Fresh, Fresh, Rotten) Redundant with critics_score
director Director of the movie Not predictive without other data
dvd_rel_day Day of the month the movie is released on DVD No predictive value
dvd_rel_month Month the movie is released on DVD No predictive value
dvd_rel_year Year the movie is released on DVD No predictive value
imdb_url Link to IMDB page for the movie No predictive value
rt_url Link to Rotten Tomatoes page for the movie No predictive value
studio The studio that produced the film Not a variable that Paramount can change
thtr_rel_day Day of the month the movie is released in theaters No predictive value
thtr_rel_year Year the movie is released in theaters No predictive value
title Title of movie No predictive value
title_type Type of movie (Documentary, Feature Film, TV Movie) Redundant with genre
top200_box Whether or not the movie is in the Top 200 Box Office list on BoxOfficeMojo (no, yes) Redundant with box office success.

The full resultant codebook for the data set can be found in Appendix A


Part 2: Research question

The underlying intent of this analysis was to determine the factors that most influence box office success for a film. Since box office revenue was not among the variables included in the raw data set, the first task was to determine which of the selected (or derived) variables would stand as a proxy for box office success. As such the first research question is concretely stated as follows:
> Which of the selected or derived variables is most highly associated / correlated with total lifetime box office revenue

Once this proxy response variable was determined, the features that are most highly associated / correlated with this response variable were examined via the following research question.
> Which features are most highly associated / correlated with the proxy response for box office success


Part 3: Exploratory data analysis

The exploratory data analysis comprised both a univariate and bivariate examination of the variables.

Univariate Analysis

Univariate Analysis of Categorical Variables

The purpose of the univariate analysis of categorical variables was to examine the relative frequencies and proportions of observations for each level of the categorical level. The categorical variables included at this stage of the analysis are indicated in Table 3.

Table 3: Categorical Variables
Variable Description
best_actor_win Whether or not one of the main actors in the movie ever won an Oscar (no, yes) – note that this is not necessarily whether the actor won an Oscar for their role in the given movie
best_actress_win Whether or not one of the main actresses in the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the actresses won an Oscar for their role in the given movie
best_dir_win Whether or not the director of the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the director won an Oscar for the given movie
best_pic_nom Whether or not the movie was nominated for a best picture Oscar (no, yes)
best_pic_win Whether or not the movie won a best picture Oscar (no, yes)
genre Genre of movie (Action & Adventure, Comedy, Documentary, Drama, Horror, Mystery & Suspense, Other)
mpaa_rating MPAA rating of the movie (G, PG, PG-13, R, Unrated)
thtr_rel_month Month the movie is released in theaters
thtr_rel_season Season the movie was released in theaters

For brevity reasons, this section briefly covers the five variables most important to the modeling effort, in priority order. The complete analysis can be found in Appendix B.

Director

The work of 503 directors was included in the sample provided for this project. Data with respect to the number of films in the sample per director were captured in the director experience variable defined in the quantitative section.

Genre

The drama genre represented a plurality of the releases in the sample, followed by comedy action & adventure then mystery & suspense. The top four genres account for nearly 80% of the films in the sample. Figure 1: Films by genre

MPAA Rating

Rated R films accounted for over 50% of the releases, followed by PG and PG-13. Collectively, R, PG, and PG-13 rated films represent 90% of the films in the sample. NC-17 films were excluded from this analysis. Figure 2: Films by MPAA Rating

Best Picture

The best picture nomination variable proved to be among the top five most influential categorical variables. Typically, variables which such inbalance would be under consideration for exclusion as it might bias the linear regression slopes. The decision in this case was to assume that with random sampling, these ratios reflected the true population proportions, and to keep the variables for further analysis during the modeling stage.

Figure 3: Best picture nominations and wins

Month of Theatrical Release

Though the plurality of features in the sample (32%) were released during the months of January, June, October and December, the distribution of theatrical release months appeared fairly balanced within the sample. Figure 4: Theatrical releases by month

Univariate Analysis of Quantitative Variables

The primary aim of this analysis was to examine the distribution of the variables vis-a-vis a normal distribution, and to identify potential outliers. Summary statistics, histograms, boxplots, normal quantile-quantile plots were rendered for each variable. The quantitative variables included at this stage of the analysis are indicated in Table 4.

Table 4: Quantitative Variables
Variable Description
audience_score Audience score on Rotten Tomatoes
box_office Box office revenue from BoxOfficeMojo.com
box_office_log Log of Box office revenue from BoxOfficeMojo.com
cast_experience The sum across all cast members for a film, of the number of films in which each actor appeared
cast_experience_log Log of the sum across all cast members for a film, of the number of films in which each actor appeared
cast_votes Total number of allocated IMDB votes for the cast of a film
cast_votes_log Log of the total number of allocated IMDB votes for the cast of a film
critics_score Critics score on Rotten Tomatoes
director_experience Total number of films in sample for a director
director_experience_log Log total number of films in sample for a director
imdb_num_votes Number of votes on IMDB
imdb_num_votes_log Log number of IMDB votes
imdb_rating Rating on IMDB
runtime Runtime of movie (in minutes)
runtime_log Log runtime of movie (in minutes)
scores 10 * IMDB Rating + critics score + audience_score
scores_log Log(10 * IMDB Rating + critics score + audience_score)
thtr_days Number of days between theatre and dvd release
thtr_days_log Log number of days between theatre and dvd release

Again, the five most influential quantitative variables are covered here in some detail. The complete analysis can be found in Appendix B.

Director Experience

This derived variable measured the relative experience of a given director and was defined as the sum of the observations for the director associated with each film.

Table 5: Director experience summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1 1 1 1.5 2 1 4 0 0.75 51.4 2.55 1.73

Figure 5: Director experience histogram and QQ Plot

Figure 6: Director experience boxplot

Central Tendency: The summary statistics (Table 5) the central tendency for director experience was 1 films and 1.5 films for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.75, corresponds with a coefficient of variation of 51.4%, indicating a high degree of dispersion.

Shape of Distribution: The sample skewness (1.73), indicated that the distribution of director experience was right-skewed. The sample kurtosis (2.55), indicated that the distribution of director experience was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 5 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 6, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 1, 2, and 1, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 3.5]. Indeed, this confirmed the existence of 20 outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Cast Experience

This derived variable measured the relative experience of a given cast and was defined as the sum of the observations for the cast associated with each film.

Table 6: Cast experience summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 5 6 7 7.5 9 3 15 0 2.16 29 0.32 0.89

Figure 7: Cast experience histogram and QQ Plot

Figure 8: Cast experience boxplot

Central Tendency: The summary statistics (Table 6) the central tendency for cast experience was 7 films and 7.5 films for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.16, corresponds with a coefficient of variation of 29%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (0.89), indicated that the distribution of cast experience was right-skewed. The sample kurtosis (0.32), indicated that the distribution of cast experience was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 7 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 8, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 6, 9, and 3, respectively. This yielded a 1.5xIQR ‘acceptable’ range [1.5, 13.5]. Indeed, this confirmed the existence of 7 outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Number of IMDB Votes

This variable captured the number of IMDB votes cast for each film.

Table 7: IMDB votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 183 5035 16511 60193.3 62773 57738 893008 0 114459.8 190.2 19.12 3.96

Figure 9: IMDB votes histogram and QQ Plot

Figure 10: IMDB votes boxplot

Central Tendency: The summary statistics (Table 7) the central tendency for imdb votes was 16,511 votes and 60,193.3 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 114,459.75, corresponds with a coefficient of variation of 190.2%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (3.96), indicated that the distribution of imdb votes was right-skewed. The sample kurtosis (19.12), indicated that the distribution of imdb votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 9 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 10, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 5,035, 62,773, and 57,738, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 149,380]. Indeed, this confirmed the existence of 67 outliers.

Log Number of IMDB Votes

This was a log transformation of the IMDB votes variable.

Table 8: Log IMDB votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 7.5 12.3 14 14.1 15.9 3.6 19.8 0 2.35 16.6 -0.56 0.03

Figure 11: Log IMDB votes histogram and QQ Plot

Figure 12: Log IMDB votes boxplot

Central Tendency: The summary statistics (Table 8) the central tendency for imdb log votes was 14 log votes and 14.1 log votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.35, corresponds with a coefficient of variation of 16.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.03), indicated that the distribution of imdb log votes was approximately symmetric. The sample kurtosis (-0.56), indicated that the distribution of imdb log votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 11 reveal a nearly normal distribution.

Outliers: The boxplot in Figure 12, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 12.3, 15.9, and 3.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.9, 21.3]. Indeed, this confirmed the existence of no outliers.

IMDB Ratings

This variable captured the IMDB rating for each film

Table 9: IMDB rating summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1.9 5.9 6.6 6.5 7.3 1.4 9 0 1.08 16.6 1.31 -0.89

Figure 13: IMDB rating histogram and QQ Plot

Figure 14: IMDB rating boxplot

Central Tendency: The summary statistics (Table 9) the central tendency for imdb rating was 6.6 points and 6.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 1.08, corresponds with a coefficient of variation of 16.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.89), indicated that the distribution of imdb rating was left-skewed. The sample kurtosis (1.31), indicated that the distribution of imdb rating was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 13 reveal a nearly normal distribution.

Outliers: The boxplot in Figure 14, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 5.9, 7.3, and 1.4, respectively. This yielded a 1.5xIQR ‘acceptable’ range [3.8, 9.4]. Indeed, this confirmed the existence of 18 outliers.

Critics Scores

This variable captured the critics scores for each film

Table 10: Critics score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1 33 61 57.4 83 50 100 0 28.37 49.4 -1.17 -0.26

Figure 15: Critics score histogram and QQ Plot

Figure 16: Critics score boxplot

Central Tendency: The summary statistics (Table 10) the central tendency for critics score was 61 points and 57.4 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28.37, corresponds with a coefficient of variation of 49.4%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.26), indicated that the distribution of critics score was approximately symmetric. The sample kurtosis (-1.17), indicated that the distribution of critics score was platykurtic or light-tailed. The histogram and QQ plot in Figure 15 reveals a left skewed distribution that departs from normality.

Outliers: The boxplot in Figure 16, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 33, 83, and 50, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 158]. Indeed, this confirmed the existence of no outliers.

Audience Scores

This variable captured the audience scores for each film

Table 11: Audience score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1 33 61 57.4 83 50 100 0 28.37 49.4 -1.17 -0.26

Figure 17: Audience score histogram and QQ Plot

Figure 18: Audience score boxplot

Central Tendency: The summary statistics (Table 11) the central tendency for audience score was 61 points and 57.4 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28.37, corresponds with a coefficient of variation of 49.4%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.26), indicated that the distribution of audience score was approximately symmetric. The sample kurtosis (-1.17), indicated that the distribution of audience score was platykurtic or light-tailed. The histogram and QQ plot in Figure 17 reveals a left skewed distribution that departs from normality.

Outliers: The boxplot in Figure 18, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 33, 83, and 50, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 158]. Indeed, this confirmed the existence of no outliers.

Cast Votes

This variable captured the total number of votes allocated to each cast member for a film.

Table 12: Cast votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 183 18552.5 78379.2 158644.9 228174.2 209621.7 1504872 0 198107.9 124.9 6.57 2.17

Figure 19: Cast votes histogram and QQ Plot

Figure 20: Cast votes boxplot

Central Tendency: The summary statistics (Table 12) the central tendency for cast votes was 78,379.2 votes and 158,644.9 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 198,107.89, corresponds with a coefficient of variation of 124.9%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (2.17), indicated that the distribution of cast votes was right-skewed. The sample kurtosis (6.57), indicated that the distribution of cast votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 19 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 20, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 18,552.5, 228,174.2, and 209,621.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 542,606.75]. Indeed, this confirmed the existence of 26 outliers.

Log Cast Votes

This is a log transformation of the cast votes variable.

Table 13: Log cast votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 7.5 14.2 16.3 15.9 17.8 3.6 20.5 0 2.46 15.5 -0.08 -0.67

Figure 21: Log cast votes histogram and QQ Plot

Figure 22: Log cast votes boxplot

Central Tendency: The summary statistics (Table 13) the central tendency for log cast votes was 16.3 log(votes) and 15.9 log(votes) for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.46, corresponds with a coefficient of variation of 15.5%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.67), indicated that the distribution of log cast votes was left-skewed. The sample kurtosis (-0.08), indicated that the distribution of log cast votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 21 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 22, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 14.2, 17.8, and 3.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [8.8, 23.2]. Indeed, this confirmed the existence of 4 outliers.

Scores

This variable captured the total score for each film defined as 10 * IMDB Rating + critics score + audience_score.

Table 10Table 11Table 14: Scores summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 38 145 187 184.5 232 87 284 0 54.52 29.6 -0.82 -0.32

Figure 15Figure 17Figure 23: Scores histogram and QQ Plot

Figure 16Figure 18Figure 24: Scores boxplot

Central Tendency: The summary statistics (Table 10Table 11Table 14) the central tendency for total scores was 187 points and 184.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 54.52, corresponds with a coefficient of variation of 29.6%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.32), indicated that the distribution of total scores was approximately symmetric. The sample kurtosis (-0.82), indicated that the distribution of total scores was platykurtic or light-tailed. The histogram and QQ plot in Figure 15Figure 17Figure 23 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 16Figure 18Figure 24, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 145, 232, and 87, respectively. This yielded a 1.5xIQR ‘acceptable’ range [14.5, 362.5]. Indeed, this confirmed the existence of no outliers.

Log Scores

This is a log transformation of scores variable.

Table 15: Log scores summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 5.2 7.2 7.5 7.5 7.9 0.7 8.1 0 0.5 6.7 1.12 -1.07

Figure 25: Log scores histogram and QQ Plot

Figure 26: Log scores boxplot

Central Tendency: The summary statistics (Table 15) the central tendency for log total scores was 7.5 points and 7.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.5, corresponds with a coefficient of variation of 6.7%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-1.07), indicated that the distribution of log total scores was left-skewed. The sample kurtosis (1.12), indicated that the distribution of log total scores was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 25 reveals a left skewed distribution that departs rather significantly from normality.

Outliers: The boxplot in Figure 26, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 7.2, 7.9, and 0.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.15, 8.95]. Indeed, this confirmed the existence of 13 outliers.

Runtime

Total lifetime was obtained for a subset of 100 randomly selected films from the movie data set. This is an analysis of runtime for this random sampling.

Table 16: Runtime summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 65 93 103 106.6 116 23 267 0 19.12 17.9 9.67 1.98

Figure 27: Runtime histogram and QQ Plot

Figure 28: Runtime boxplot

Central Tendency: The summary statistics (Table 16) the central tendency for runtime was 103 minutes and 106.6 minutes for the median and mean, respectively.

Dispersion: The standard deviation, s = 19.12, corresponds with a coefficient of variation of 17.9%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (1.98), indicated that the distribution of runtime was right-skewed. The sample kurtosis (9.67), indicated that the distribution of runtime was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 27 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 28, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 93, 116, and 23, respectively. This yielded a 1.5xIQR ‘acceptable’ range [58.5, 150.5]. Indeed, this confirmed the existence of 16 outliers.

Theatre Days

This variable captured the number of days between theatrical and dvd release

Table 17: Theatre says summary statistics

Figure 29: Theatre days histogram and QQ Plot

NULL

Figure 30: Theatre days boxplot

Central Tendency: The summary statistics (Table 17)

Dispersion:

Shape of Distribution: The histogram and QQ plot in Figure 29 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 30, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant.

Box Office

Total lifetime box office revenue was obtained for a subset of 100 randomly selected films from the movie data set. This is an analysis of box office revenue for this random sampling.

Table 18: Box office revenue summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
231 2749 1064483 13349927 38611880 49655390 48590907 658672302 0 68922521 178.5 31.2 4.55

Figure 31: Box office revenue histogram and QQ Plot

Figure 32: Box office revenue boxplot

Central Tendency: The summary statistics (Table 18) the central tendency for box office was 13,349,927 dollars and 38,611,879.9 dollars for the median and mean, respectively.

Dispersion: The standard deviation, s = 68,922,520.54, corresponds with a coefficient of variation of 178.5%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (4.55), indicated that the distribution of box office was right-skewed. The sample kurtosis (31.2), indicated that the distribution of box office was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 31 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 32, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 1,064,483, 49,655,390, and 48,590,907, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 122,541,750.5]. Indeed, this confirmed the existence of 21 outliers.

Log Box Office

This is a log transformation of the box office variable.

Table 19: Log box office revenue summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
231 11.4 20 23.7 22.6 25.6 5.5 29.3 0 3.84 17 -0.21 -0.8

Figure 33: Log box office revenue histogram and QQ Plot

Figure 34: Log box office revenue boxplot

Central Tendency: The summary statistics (Table 19) the central tendency for log box office was 23.7 log(dollars) and 22.6 log(dollars) for the median and mean, respectively.

Dispersion: The standard deviation, s = 3.84, corresponds with a coefficient of variation of 17%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.8), indicated that the distribution of log box office was left-skewed. The sample kurtosis (-0.21), indicated that the distribution of log box office was platykurtic or light-tailed. The histogram and QQ plot in Figure 33 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 34, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 20, 25.6, and 5.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [11.75, 33.85]. Indeed, this confirmed the existence of 1 outliers.

Bivariate Analysis

Dependent Variable

As mentioned above, the first objective was to identify an available variable that would proxy for box office success. Correlation tests were conducted between the quantitative variables and the log of box office revenue. The top 5 variables most highly correlated with log of box office revenue are summarized in Table 20.

Table 20 Top 5 variables most highly correlated with box office revenue
Variable Correlation Statistic df p.value X95..CI
imdb_num_votes_log 0.69 14.31 229 < 0.05 [ 0.61 , 0.75 ]
cast_votes_log 0.57 10.39 229 < 0.05 [ 0.47 , 0.65 ]
imdb_num_votes 0.47 8.04 229 < 0.05 [ 0.36 , 0.56 ]
cast_votes 0.46 7.82 229 < 0.05 [ 0.35 , 0.56 ]
cast_experience_log 0.39 6.38 229 < 0.05 [ 0.27 , 0.49 ]
cast_experience 0.37 6.01 229 < 0.05 [ 0.25 , 0.48 ]
director_experience_log 0.27 4.20 229 < 0.05 [ 0.14 , 0.38 ]
runtime 0.26 4.12 229 < 0.05 [ 0.14 , 0.38 ]
runtime_log 0.26 4.04 229 < 0.05 [ 0.13 , 0.37 ]
director_experience 0.25 3.89 229 < 0.05 [ 0.12 , 0.37 ]

Figure 35: Scatterplots of variables most highly correlated with log of box office revenue

The scatter plots in Figure 35, confirmed it. The log of the number of IMDB votes would proxy for box office revenue and correlation with this dependent variable was the focus of the bivariate analysis that follows.

Categorical Variable Analysis

Association tests were conducted between the categorical variables and the log number of IMDB votes and Table 21 summarizes the most highly associated variables.

Table 21 Categorical variables most highly associated with the log number of IMDB votes.
Dependent Independent R.squared F.value p.value
Log IMDB Votes genre 0.16 11.18 < 0.05
Log IMDB Votes mpaa_rating 0.11 18.57 < 0.05
Log IMDB Votes best_pic_nom 0.05 33.36 < 0.05
Log IMDB Votes thtr_rel_month 0.03 1.92 < 0.05
Log IMDB Votes best_pic_win 0.03 21.15 < 0.05
Log IMDB Votes best_dir_win 0.03 20.99 < 0.05
Log IMDB Votes thtr_rel_season 0.03 4.32 < 0.05
Log IMDB Votes best_actor_win 0.02 11.69 < 0.05
Log IMDB Votes best_actress_win 0.01 6.02 < 0.05

As expected, director and studio were highly associated with film popularity.

Quantitative Variable Analysis

The correlations between the quantitative variables and the log number of IMDB votes are listed in Table 22 in order of highest to lowest correlation.

Table 22 Top quantitative variables most highly correlated with the log number of IMDB votes.

The log of cast votes was highly correlated with the log number of IMDB votes; whereas cast experience was significantly less correlated. Surprisingly, the number of days between the dvd release and the theatrical release was negatively correlated with IMDB votes, causing one to consider the proportion of IMDB votes cast by DVD viewers.


Part 4: Modeling

Developing a linear model that can be used to effectively predict box office performance is the focus of this section. As such, full model feature selection, model selection, model diagnostics, and model interpretation are covered here in detail.

Full Model Feature Selection.

In the prior section, association and correlation tests were conducted with a 95% confidence level. All categorical variables would remain in the model. The following quantitative variables were removed because they were redundant with other variables with higher correlation with dependent variable:
* cast_experience - redundant with the log of caset experience
* cast_votes - redundant with cast_votes_log, which has a higher correlation
* director_experience - redundant with the log transformation of director experience
* imdb_num_votes - redundant with the dependent variable, its log transformation
* imdb_rating - redundant aspect of movie performance. * runtime - redundant with runtime log variable
* scores_log - redundant with the scores variable
* thtr_days - redundant with the log transformation of the thtr_days variable
* scores - redundant with IMDB rating * audience score - redundant with IMDB rating

Thus, the full model is presented.

Table 23: Full Model
Variable Type Measure Value p.value
genre Categorical R-squared 0.16 < 0.05
mpaa_rating Categorical R-squared 0.11 < 0.05
best_pic_nom Categorical R-squared 0.05 < 0.05
thtr_rel_month Categorical R-squared 0.03 < 0.05
best_pic_win Categorical R-squared 0.03 < 0.05
best_dir_win Categorical R-squared 0.03 < 0.05
thtr_rel_season Categorical R-squared 0.03 < 0.05
best_actor_win Categorical R-squared 0.02 < 0.05
best_actress_win Categorical R-squared 0.01 < 0.05

Model Selection

Starting with the full model described above, both forward selection and backward elimination methods were employed to determine if two different models emerged from the process, then to evaluate the performance of those models.

Forward Selection

The forward selection process begins with a null model then all variables are added to the model, one-by-one, and the model that provides the greatest improvement in adjusted R-squared is selected. If the adjusted R-squared for this set was greater than the best R-squared for the model, it was selected. The process repeats until all predictors were evaluated. Table 24 provides the the forward selection process and the summary statistics for each step.

Table 24: Forward Selection Prediction Model
Step Selected Model.Size DF F.statistic R.Squared Adjusted.R2 p.value Pct Chg
1 cast_votes_log 1 610 808.90 0.57 0.57 0 0.00
2 cast_experience_log 2 609 487.70 0.62 0.61 0 7.91
3 thtr_days_log 3 608 348.09 0.63 0.63 0 2.61
4 genre 4 598 85.67 0.65 0.64 0 2.06
5 critics_score 5 597 91.62 0.68 0.68 0 4.98
6 best_pic_nom 6 596 89.02 0.69 0.68 0 1.33
7 director_experience_log 7 595 85.09 0.70 0.69 0 0.58
8 thtr_rel_season 8 591 69.11 0.70 0.69 0 0.29
9 runtime_log 9 590 66.58 0.70 0.69 0 0.43
10 best_pic_win 10 589 63.90 0.70 0.69 0 0.14

Table 24 Forward Selection Process

Model Overview

The model is summarized as follows:

\[y_i\]

Table 25: Backward Elimination Prediction Model


Part 5: Prediction

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Part 6: Conclusion

Appendix

Appendix A: Codebook

Table 26: Movie data set codebook
Source Type Variable Description
General
IMDB/RT/BO Categorical actor1 First main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical actor2 Second main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical actor3 Third main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical actor4 Fourth main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical actor5 Fifth main actor/actress in the abridged cast of the movie
IMDB/RT/BO Categorical audience_rating Categorical variable for audience rating on Rotten Tomatoes (Spilled, Upright)
IMDB/RT/BO Categorical critics_rating Categorical variable for critics rating on Rotten Tomatoes (Certified Fresh, Fresh, Rotten)
Organization
IMDB/RT/BO Categorical dvd_rel_day Day of the month the movie is released on DVD
IMDB/RT/BO Categorical dvd_rel_month Month the movie is released on DVD
IMDB/RT/BO Categorical dvd_rel_year Year the movie is released on DVD
IMDB/RT/BO Categorical imdb_url Link to IMDB page for the movie
IMDB/RT/BO Categorical rt_url Link to Rotten Tomatoes page for the movie
IMDB/RT/BO Categorical thtr_rel_day Day of the month the movie is released in theaters
IMDB/RT/BO Categorical thtr_rel_year Year the movie is released in theaters
Dates
IMDB/RT/BO Categorical title Title of movie
IMDB/RT/BO Categorical best_actor_win Whether or not one of the main actors in the movie ever won an Oscar (no, yes) – note that this is not necessarily whether the actor won an Oscar for their role in the given movie
IMDB/RT/BO Categorical best_actress_win Whether or not one of the main actresses in the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the actresses won an Oscar for their role in the given movie
IMDB/RT/BO Categorical best_dir_win Whether or not the director of the movie ever won an Oscar (no, yes) – not that this is not necessarily whether the director won an Oscar for the given movie
IMDB/RT/BO Categorical best_pic_nom Whether or not the movie was nominated for a best picture Oscar (no, yes)
IMDB/RT/BO Categorical best_pic_win Whether or not the movie won a best picture Oscar (no, yes)
IMDB/RT/BO Categorical director Director of the movie
Experience
IMDB/RT/BO Categorical genre Genre of movie (Action & Adventure, Comedy, Documentary, Drama, Horror, Mystery & Suspense, Other)
IMDB/RT/BO Categorical mpaa_rating MPAA rating of the movie (G, PG, PG-13, R, Unrated)
Performance
IMDB/RT/BO Categorical studio The studio that produced the film
IMDB/RT/BO Categorical thtr_rel_month Month the movie is released in theaters
Derived Categorical thtr_rel_season Season the movie was released in theaters
IMDB/RT/BO Categorical title_type Type of movie (Documentary, Feature Film, TV Movie)
IMDB/RT/BO Categorical top200_box Whether or not the movie is in the Top 200 Box Office list on BoxOfficeMojo (no, yes)
IMDB/RT/BO Numeric audience_score Audience score on Rotten Tomatoes
Derived Numeric box_office Box office revenue from BoxOfficeMojo.com
Derived Numeric box_office_log Log of Box office revenue from BoxOfficeMojo.com
Derived Numeric cast_experience The sum across all cast members for a film, of the number of films in which each actor appeared
Derived Numeric cast_experience_log Log of the sum across all cast members for a film, of the number of films in which each actor appeared
Derived Numeric cast_votes Total number of allocated IMDB votes for the cast of a film
Derived Numeric cast_votes_log Log of the total number of allocated IMDB votes for the cast of a film
IMDB/RT/BO Numeric critics_score Critics score on Rotten Tomatoes
Derived Numeric director_experience Total number of films in sample for a director
Derived Numeric director_experience_log Log total number of films in sample for a director
Interaction
IMDB/RT/BO Numeric imdb_num_votes Number of votes on IMDB
Derived Numeric imdb_num_votes_log Log number of IMDB votes
Box Office
IMDB/RT/BO Numeric imdb_rating Rating on IMDB
IMDB/RT/BO Numeric runtime Runtime of movie (in minutes)
Derived Numeric runtime_log Log runtime of movie (in minutes)
Derived Numeric scores 10 * IMDB Rating + critics score + audience_score
Derived Numeric scores_log Log(10 * IMDB Rating + critics score + audience_score)
Derived Numeric thtr_days Number of days between theatre and dvd release
Derived Numeric thtr_days_log Log number of days between theatre and dvd release

Appendix B: Univariate Analysis

Best Director / Actor / Actress

As indicated in Figure 36, the percentages of films with best director, actor and actress oscars were 7%, 15%, and 12%, respectively. Again, the decision in this case was to assume that with random sampling, these ratios reflected the true population proportions, and to keep the variables for further analysis during the modeling stage.

Figure 36: Best director/actor/actress

Best Picture

Since the proportion of films nominated for and winning best picture were so small, this variable was not likely to be a good predictor of movie popularity. The bivariate analysis below will illuminate this further.

Figure 37: Best picture nominations and wins

Genre

The drama genre represented a plurality of the releases in the sample, followed by comedy action & adventure then mystery & suspense. The top four genres account for nearly 80% of the films in the sample. Figure 38: Films by genre

MPAA Rating

Rated R films accounted for over 0% of the releases, followed by PG and PG-13. Collectively, R, PG, and PG-13 rated films represent 90% of the films in the sample. NC-17 films were excluded from this analysis. Figure 39: Films by MPAA Rating

Month of Theatrical Release

Though the plurality of features in the sample (32%) were released during the months of January, June, October and December, the distribution of theatrical release months appeared fairly balanced within the sample. Figure 40: Theatrical releases by month

Season of Theatrical Release

The plurality of features in the sample were released during the fall and summer months with over 20% opening in the month of December alone. Figure 41: Theatrical releases by season

Audience Scores

This variable captured the audience scores from Rotten Tomatoes for each film

Table 27: Audience score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1 33 61 57.4 83 50 100 0 28.37 49.4 -1.17 -0.26

Figure 42: Audience score histogram and QQ Plot

Figure 43: Audience score boxplot

Central Tendency: The summary statistics (Table 27) the central tendency for audience score was 61 points and 57.4 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28.37, corresponds with a coefficient of variation of 49.4%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.26), indicated that the distribution of audience score was approximately symmetric. The sample kurtosis (-1.17), indicated that the distribution of audience score was platykurtic or light-tailed. The histogram and QQ plot in Figure 42 reveals a left skewed distribution that departs from normality.

Outliers: The boxplot in Figure 43, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 33, 83, and 50, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 158]. Indeed, this confirmed the existence of no outliers.

Box Office

Total lifetime box office revenue was obtained for a subset of 100 randomly selected films from the movie data set. This is an analysis of box office revenue for this random sampling.

Table 28: Box office revenue summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
231 2749 1064483 13349927 38611880 49655390 48590907 658672302 0 68922521 178.5 31.2 4.55

Figure 44: Box office revenue histogram and QQ Plot

Figure 45: Box office revenue boxplot

Central Tendency: The summary statistics (Table 28) the central tendency for box office was 13,349,927 dollars and 38,611,879.9 dollars for the median and mean, respectively.

Dispersion: The standard deviation, s = 68,922,520.54, corresponds with a coefficient of variation of 178.5%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (4.55), indicated that the distribution of box office was right-skewed. The sample kurtosis (31.2), indicated that the distribution of box office was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 44 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 45, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 1,064,483, 49,655,390, and 48,590,907, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 122,541,750.5]. Indeed, this confirmed the existence of 21 outliers.

Log Box Office

This is a log transformation of the box office variable.

Table 29: Log box office revenue summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
231 11.4 20 23.7 22.6 25.6 5.5 29.3 0 3.84 17 -0.21 -0.8

Figure 46: Log box office revenue histogram and QQ Plot

Figure 47: Log box office revenue boxplot

Central Tendency: The summary statistics (Table 29) the central tendency for log box office was 23.7 log(dollars) and 22.6 log(dollars) for the median and mean, respectively.

Dispersion: The standard deviation, s = 3.84, corresponds with a coefficient of variation of 17%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.8), indicated that the distribution of log box office was left-skewed. The sample kurtosis (-0.21), indicated that the distribution of log box office was platykurtic or light-tailed. The histogram and QQ plot in Figure 46 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 47, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 20, 25.6, and 5.5, respectively. This yielded a 1.5xIQR ‘acceptable’ range [11.75, 33.85]. Indeed, this confirmed the existence of 1 outliers.

Cast Experience

This derived variable measured the relative experience of a given cast and was defined as the sum of the observations for the cast associated with each film.

Table 30: Cast experience summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 5 6 7 7.5 9 3 15 0 2.16 29 0.32 0.89

Figure 48: Cast experience histogram and QQ Plot

Figure 49: Cast experience boxplot

Central Tendency: The summary statistics (Table 30) the central tendency for cast experience was 7 films and 7.5 films for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.16, corresponds with a coefficient of variation of 29%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (0.89), indicated that the distribution of cast experience was right-skewed. The sample kurtosis (0.32), indicated that the distribution of cast experience was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 48 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 49, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 6, 9, and 3, respectively. This yielded a 1.5xIQR ‘acceptable’ range [1.5, 13.5]. Indeed, this confirmed the existence of 7 outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Log Cast Experience

This variable is a log transformation of the cast experience variable

Table 31: Cast experience summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 2.3 2.6 2.8 2.8 3.2 0.6 3.9 0 0.4 14 -0.72 0.36

Figure 50: Cast experience histogram and QQ Plot

Figure 51: Cast experience boxplot

Central Tendency: The summary statistics (Table 31) the central tendency for cast experience was 2.8 log(films) and 2.8 log(films) for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.4, corresponds with a coefficient of variation of 14%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.36), indicated that the distribution of cast experience was approximately symmetric. The sample kurtosis (-0.72), indicated that the distribution of cast experience was platykurtic or light-tailed. The histogram and QQ plot in Figure 50 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 51, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 2.6, 3.2, and 0.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [1.7, 4.1]. Indeed, this confirmed the existence of no outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Cast Votes

This variable captured the total number of votes allocated to each cast member for a film.

Table 32: Cast votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 183 18552.5 78379.2 158644.9 228174.2 209621.7 1504872 0 198107.9 124.9 6.57 2.17

Figure 52: Cast votes histogram and QQ Plot

Figure 53: Cast votes boxplot

Central Tendency: The summary statistics (Table 32) the central tendency for cast votes was 78,379.2 votes and 158,644.9 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 198,107.89, corresponds with a coefficient of variation of 124.9%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (2.17), indicated that the distribution of cast votes was right-skewed. The sample kurtosis (6.57), indicated that the distribution of cast votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 52 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 53, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 18,552.5, 228,174.2, and 209,621.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 542,606.75]. Indeed, this confirmed the existence of 26 outliers.

Log Cast Votes

This is a log transformation of the cast votes variable.

Table 33: Log cast votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 7.5 14.2 16.3 15.9 17.8 3.6 20.5 0 2.46 15.5 -0.08 -0.67

Figure 54: Log cast votes histogram and QQ Plot

Figure 55: Log cast votes boxplot

Central Tendency: The summary statistics (Table 33) the central tendency for log cast votes was 16.3 log(votes) and 15.9 log(votes) for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.46, corresponds with a coefficient of variation of 15.5%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.67), indicated that the distribution of log cast votes was left-skewed. The sample kurtosis (-0.08), indicated that the distribution of log cast votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 54 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 55, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 14.2, 17.8, and 3.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [8.8, 23.2]. Indeed, this confirmed the existence of 4 outliers.

Critics Scores

This variable captured the critics scores for each film

Table 34: Critics score summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1 33 61 57.4 83 50 100 0 28.37 49.4 -1.17 -0.26

Figure 56: Critics score histogram and QQ Plot

Figure 57: Critics score boxplot

Central Tendency: The summary statistics (Table 34) the central tendency for critics score was 61 points and 57.4 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 28.37, corresponds with a coefficient of variation of 49.4%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.26), indicated that the distribution of critics score was approximately symmetric. The sample kurtosis (-1.17), indicated that the distribution of critics score was platykurtic or light-tailed. The histogram and QQ plot in Figure 56 reveals a left skewed distribution that departs from normality.

Outliers: The boxplot in Figure 57, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 33, 83, and 50, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 158]. Indeed, this confirmed the existence of no outliers.

Director Experience

This derived variable measured the relative experience of a given director and was defined as the sum of the observations for the director associated with each film.

Table 35: Director experience summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1 1 1 1.5 2 1 4 0 0.75 51.4 2.55 1.73

Figure 58: Director experience histogram and QQ Plot

Figure 59: Director experience boxplot

Central Tendency: The summary statistics (Table 35) the central tendency for director experience was 1 films and 1.5 films for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.75, corresponds with a coefficient of variation of 51.4%, indicating a high degree of dispersion.

Shape of Distribution: The sample skewness (1.73), indicated that the distribution of director experience was right-skewed. The sample kurtosis (2.55), indicated that the distribution of director experience was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 58 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 59, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 1, 2, and 1, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 3.5]. Indeed, this confirmed the existence of 20 outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Log Director Experience

This variable was a log transformation of the director experience variable.

Table 36: Log director experience summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 0 0 0 0.4 1 1 2 0 0.6 149.8 -0.09 1.11

Figure 60: Log director experience histogram and QQ Plot

Figure 61: Log director experience boxplot

Central Tendency: The summary statistics (Table 36) the central tendency for director experience was 0 log(films) and 0.4 log(films) for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.6, corresponds with a coefficient of variation of 149.8%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (1.11), indicated that the distribution of director experience was right-skewed. The sample kurtosis (-0.09), indicated that the distribution of director experience was platykurtic or light-tailed. The histogram and QQ plot in Figure 60 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 61, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 0, 1, and 1, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 2.5]. Indeed, this confirmed the existence of no outliers. Given the proximity of the outliers to the 1.5xIQR, no effort was made to remove them.

Number of IMDB Votes

This variable captured the number of IMDB votes cast for each film.

Table 37: IMDB votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 183 5035 16511 60193.3 62773 57738 893008 0 114459.8 190.2 19.12 3.96

Figure 62: IMDB votes histogram and QQ Plot

Figure 63: IMDB votes boxplot

Central Tendency: The summary statistics (Table 37) the central tendency for imdb votes was 16,511 votes and 60,193.3 votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 114,459.75, corresponds with a coefficient of variation of 190.2%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (3.96), indicated that the distribution of imdb votes was right-skewed. The sample kurtosis (19.12), indicated that the distribution of imdb votes was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 62 reveal a distribution which departs significantly from normality.

Outliers: The boxplot in Figure 63, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 5,035, 62,773, and 57,738, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 149,380]. Indeed, this confirmed the existence of 67 outliers.

Log Number of IMDB Votes

This was a log transformation of the IMDB votes variable.

Table 38: Log IMDB votes summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 7.5 12.3 14 14.1 15.9 3.6 19.8 0 2.35 16.6 -0.56 0.03

Figure 64: Log IMDB votes histogram and QQ Plot

Figure 65: Log IMDB votes boxplot

Central Tendency: The summary statistics (Table 38) the central tendency for imdb log votes was 14 log votes and 14.1 log votes for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.35, corresponds with a coefficient of variation of 16.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.03), indicated that the distribution of imdb log votes was approximately symmetric. The sample kurtosis (-0.56), indicated that the distribution of imdb log votes was platykurtic or light-tailed. The histogram and QQ plot in Figure 64 reveal a nearly normal distribution.

Outliers: The boxplot in Figure 65, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 12.3, 15.9, and 3.6, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.9, 21.3]. Indeed, this confirmed the existence of no outliers.

IMDB Ratings

This variable captured the IMDB rating for each film

Table 39: IMDB rating summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1.9 5.9 6.6 6.5 7.3 1.4 9 0 1.08 16.6 1.31 -0.89

Figure 66: IMDB rating histogram and QQ Plot

Figure 67: IMDB rating boxplot

Central Tendency: The summary statistics (Table 39) the central tendency for imdb rating was 6.6 points and 6.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 1.08, corresponds with a coefficient of variation of 16.6%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-0.89), indicated that the distribution of imdb rating was left-skewed. The sample kurtosis (1.31), indicated that the distribution of imdb rating was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 66 reveal a nearly normal distribution.

Outliers: The boxplot in Figure 67, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 5.9, 7.3, and 1.4, respectively. This yielded a 1.5xIQR ‘acceptable’ range [3.8, 9.4]. Indeed, this confirmed the existence of 18 outliers.

Runtime

This is an analysis of moving runtimes.

Table 40: Runtime summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 65 93 103 106.6 116 23 267 0 19.12 17.9 9.67 1.98

Figure 68: Runtime histogram and QQ Plot

Figure 69: Runtime boxplot

Central Tendency: The summary statistics (Table 40) the central tendency for runtime was 103 minutes and 106.6 minutes for the median and mean, respectively.

Dispersion: The standard deviation, s = 19.12, corresponds with a coefficient of variation of 17.9%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (1.98), indicated that the distribution of runtime was right-skewed. The sample kurtosis (9.67), indicated that the distribution of runtime was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 68 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 69, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 93, 116, and 23, respectively. This yielded a 1.5xIQR ‘acceptable’ range [58.5, 150.5]. Indeed, this confirmed the existence of 16 outliers.

Log Runtime

This is an analysis of the log of moving runtimes.

Table 41: Log runtime summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 6 6.5 6.7 6.7 6.9 0.3 8.1 0 0.24 3.5 2.06 0.86

Figure 70: Log runtime histogram and QQ Plot

Figure 71: Log runtime boxplot

Central Tendency: The summary statistics (Table 41) the central tendency for log runtime was 6.7 minutes and 6.7 minutes for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.24, corresponds with a coefficient of variation of 3.5%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (0.86), indicated that the distribution of log runtime was right-skewed. The sample kurtosis (2.06), indicated that the distribution of log runtime was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 70 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 71, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 6.5, 6.9, and 0.3, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.05, 7.35]. Indeed, this confirmed the existence of 9 outliers.

Scores

This variable captured the total score for each film defined as 10 * IMDB Rating + critics score + audience_score.

Table 42: Scores summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 38 145 187 184.5 232 87 284 0 54.52 29.6 -0.82 -0.32

Figure 72: Scores histogram and QQ Plot

Figure 73: Scores boxplot

Central Tendency: The summary statistics (Table 42) the central tendency for total scores was 187 points and 184.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 54.52, corresponds with a coefficient of variation of 29.6%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (-0.32), indicated that the distribution of total scores was approximately symmetric. The sample kurtosis (-0.82), indicated that the distribution of total scores was platykurtic or light-tailed. The histogram and QQ plot in Figure 72 reveals a left skewed distribution that approximates normality.

Outliers: The boxplot in Figure 73, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 145, 232, and 87, respectively. This yielded a 1.5xIQR ‘acceptable’ range [14.5, 362.5]. Indeed, this confirmed the existence of no outliers.

Log Scores

This is a log transformation of scores variable.

Table 43: Log scores summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 5.2 7.2 7.5 7.5 7.9 0.7 8.1 0 0.5 6.7 1.12 -1.07

Figure 74: Log scores histogram and QQ Plot

Figure 75: Log scores boxplot

Central Tendency: The summary statistics (Table 43) the central tendency for log total scores was 7.5 points and 7.5 points for the median and mean, respectively.

Dispersion: The standard deviation, s = 0.5, corresponds with a coefficient of variation of 6.7%, indicating a low degree of dispersion.

Shape of Distribution: The sample skewness (-1.07), indicated that the distribution of log total scores was left-skewed. The sample kurtosis (1.12), indicated that the distribution of log total scores was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 74 reveals a left skewed distribution that departs rather significantly from normality.

Outliers: The boxplot in Figure 75, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 7.2, 7.9, and 0.7, respectively. This yielded a 1.5xIQR ‘acceptable’ range [6.15, 8.95]. Indeed, this confirmed the existence of 13 outliers.

Theatre Days

This variable captured the number of days between theatrical and dvd release

Table 44: Theatre says summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 1 132 391 2304.5 3910 3778 12309 0 3118.24 135.3 0.62 1.34

Figure 76: Theatre days histogram and QQ Plot

Figure 77: Theatre days boxplot

Central Tendency: The summary statistics (Table 44) the central tendency for days in theatre was 391 days and 2,304.5 days for the median and mean, respectively.

Dispersion: The standard deviation, s = 3,118.24, corresponds with a coefficient of variation of 135.3%, indicating a very high degree of dispersion.

Shape of Distribution: The sample skewness (1.34), indicated that the distribution of days in theatre was right-skewed. The sample kurtosis (0.62), indicated that the distribution of days in theatre was leptokurtic or heavy-tailed. The histogram and QQ plot in Figure 76 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 77, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that outliers were extant. The 25%, 75%, and IQR were 132, 3,910, and 3,778, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 9,577]. Indeed, this confirmed the existence of 28 outliers.

Theatre Days

This variable captured the number of days between theatrical and dvd release

Table 45: Log number of theatre days summary statistics
N Min Q1 Median Mean Q3 IQR Max NA.s SD CV Kurtosis Skewness
617 0 7 8.6 9.3 11.9 4.9 13.6 0 2.53 27.2 -1.16 0.18

Figure 78: Log number of theatre days histogram and QQ Plot

Figure 79: Log number of theatre days boxplot

Central Tendency: The summary statistics (Table 45) the central tendency for days in theatre was 8.6 days and 9.3 days for the median and mean, respectively.

Dispersion: The standard deviation, s = 2.53, corresponds with a coefficient of variation of 27.2%, indicating a moderate degree of dispersion.

Shape of Distribution: The sample skewness (0.18), indicated that the distribution of days in theatre was approximately symmetric. The sample kurtosis (-1.16), indicated that the distribution of days in theatre was platykurtic or light-tailed. The histogram and QQ plot in Figure 78 reveals a left skewed distribution that departs significantly from normality.

Outliers: The boxplot in Figure 79, which graphically depicts the median, the IQR, and maximum and minimum values, suggested that no outliers were extant. The 25%, 75%, and IQR were 7, 11.9, and 4.9, respectively. This yielded a 1.5xIQR ‘acceptable’ range [0, 19.25]. Indeed, this confirmed the existence of no outliers.

Appendix C: Bivariate Analysis

Appendix D: Multivariate Analysis

Appendix E: Modeling

Appendix F: Prediction

Appendix G: Source Code

References

John James jjames@datasciencesalon.org

15 November, 2017